Do different speaker stands can really make a big sound improvement?

Do not forget stand must provide stability also.

A fallen speaker often results in dents, dings, and damage

I use Sound Anchors with my P3esr speakers.  The stands helped focus the sound and improved imaging.  I changed out the floor spikes with round headed carriage bold to avoid punching holes in my composite vinyl flooring (selected for acoustical damping;  the flooring is on solid concrete).  The speakers sit on small sorbothane pads on the corners.  With the carriage bolts installed I can drag out the speakers for a near-field experience when I want to, which increased involvement at the expense of a slight inconvenience.

I would recommend open-frame stands for all the other Harbeths, but the P3s work great on the solid stands.

Much also depends on type of speakers you are using.   Found that Maggies blom with the added rigid support of Mye stands.  The Maggie community has embraced them and recommended as the most bang for the buck upgrade  you can acquire.

If you have a mid fi audio system (seems most folks here do) speaker stands won’t  make much difference. 
 

if you have an entry level or better high end audio system speaker stands can make significant difference. 

I could suggest a material for a Speaker Stand that will be beneficial material if the support structure to be produced from it is produced to be vert rigid structure.

Before considering different materials for a Speaker Support, the Support Plinth itself for the Speaker Stands when done correct, will bring substantial sonic improvements.

As DIYer I find multi tier plinths to be able to really allow the Speakers Cabinetry to get out of the way, in relation to influencing the end sound.